Could Regressing a Stationary Series on a Non-Stationary Series Obtain Meaningful Outcomes?

Wing-Keung Wong and Mu Yue
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Wing-Keung Wong: Department of Finance and Big Data Research Center, Asia University, Taiwan2Department of Medical Research, China Medical University Hospital, Taiwan3Business, Economic and Public Policy Research Centre, Hong Kong Shue Yan University, Hong Kong
Mu Yue: School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

Annals of Financial Economics (AFE), 2024, vol. 19, issue 03, 1-16

Abstract: We have read many papers in the literature and found that some papers report results of regressing a stationary time series on a non-stationary time series (we call it the IOI1 model). However, very few studies, if there are any, examine the IOI1 model and the robustness of inference in such settings remains an open question. To bridge the gap in the literature, in this paper, we investigate whether regressing a stationary time series, Yt, on a non-stationary time series, Xt (that is, Yt=α+βXt+ut) could get any meaningful result. To do so, we first conduct a simulation and find regressing a stationary time series on a non-stationary time series could be spurious. Thereafter, we develop the estimation and testing theory for the I0I1 model and find that the statistics TNβ for testing H0β:β=β0 versus H1β:β≠β0 from the traditional regression model (we call it IOI0 model) does not have any asymptote distribution with E(TNβ)→∞ and Var(TNβ)→∞ as N→∞, and thus, it cannot be used for the I0I1 model. We have found other interesting results as shown in our paper. Thus, our paper extends the spurious regression literature to cover a previously unexplored case, thereby contributing to a more comprehensive understanding of time series modeling and inference.

Keywords: Cointegration; stationarity; non-stationarity; regression; time series analysis (search for similar items in EconPapers)
JEL-codes: C01 C15 C22 C58 C60 (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S2010495224500118

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